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. 2016 Nov 3:6:36038.
doi: 10.1038/srep36038.

Human vision is determined based on information theory

Alfonso Delgado-Bonal  1   2 , Javier Martín-Torres  1   3
Affiliations

Human vision is determined based on information theory

Alfonso Delgado-Bonal et al. Sci Rep. .

Abstract

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.

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Figures

Figure 1
Figure 1. Optimal Information Wavelength.
Schematic representation of the distributions of the energy and entropy of radiation for a blackbody at 5800 K. The maxima of the two distributions occur at different wavelengths, 500 nm for energy and 518 for entropy. The maximum information efficiency wavelength is defined as the position at which the product of both distributions is maximized, and corresponds in this case to 508 nm. The value of the wavelengths is dependent only on the temperature, and does not include atmospheric effects such as scattering (see supplementary material).
Figure 2
Figure 2
(left): Entropy content in radiation.The normalized distributions of energy and entropy are schematically represented for blackbody at 300 K. The entropy content in radiation ratio is not uniform, and it is unity for a certain value between the maxima of both distributions. The entropy content beyond this point is monotonically increasing. (right): Entropic regions and optimal information wavelength boundary. Entropic spectral regions as a function of the wavelength and temperature of the blackbody. As a consequence of the different location of the maxima, the spectra is divided in regions where normalized entropy is below the energy (blue region) or above the energy (white region). The separation of these regions is determined by the function λT = 2.94923 × 10−3 m K (see supplementary material). The region for 5800 K blackbody is zoomed in, corresponding to our Sun.
Figure 3
Figure 3. Wien’s peak for the entropy of radiation.
The distribution of the entropy of radiation is different from the energy distribution. Its maximum (dS/dλ = 0) leads to a transcendental equation after the substitution formula image which is numerically solved: formula image. The solution gives x = 4.7912673578, and undoing the change of variable the relation λT = 3.00292 × 10−3 m K is obtained.
See this image and copyright information in PMC

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